Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

More Books:

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Language: en
Pages: 342
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2013-03-29 - Publisher: Springer Science & Business Media

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals
Lyapunov Functionals and Stability of Stochastic Difference Equations
Language: en
Pages: 370
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2011-06-02 - Publisher: Springer Science & Business Media

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. Lyapunov Functionals and Stability of
Mathematical Methods in Engineering and Applied Sciences
Language: en
Pages: 294
Authors: Hemen Dutta
Categories: Technology & Engineering
Type: BOOK - Published: 2020-01-03 - Publisher: CRC Press

This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences. Presents theory, methods, and applications
Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations
Language: en
Pages: 590
Authors: Leonid Berezansky, Alexander Domoshnitsky, Roman Koplatadze
Categories: Mathematics
Type: BOOK - Published: 2020-05-18 - Publisher: CRC Press

Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The
Optimal Control of Stochastic Difference Volterra Equations
Language: en
Pages: 220
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2014-11-27 - Publisher: Springer

This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be